Casein micelle structure: Models and muddles

Abstract

Various models of the assembly and structure of the casein micelle are critically reviewed. The subunit and Holt models are revealed to be products of muddled thinking and subject to rigid constraints and restrictions, or in the case of the Holt model guilty of serious omission. Both are shown to be particular cases of the dual-binding model when these restrictions are lifted and the omissions made good.

Full text

Casein micelle structure: Models and muddles
David S. Horne
Formerly of Hannah Research Institute, Ayr, KA6 5HL, Scotland, UK
Available online 27 December 2005
Abstract
Various models of the assembly and structure of the casein micelle are critically reviewed. The subunit and Holt models are revealed to be
products of muddled thinking and subject to rigid constraints and restrictions, or in the case of the Holt model guilty of serious omission. Both are
shown to be particular cases of the dual-binding model when these restrictions are lifted and the omissions made good.
D2005 Elsevier Ltd. All rights reserved.
Keywords: Caseins; Casein micelle models; Casein micelle structure; Micellar calcium phosphate; Hydrophobic interactions; Calcium phosphate nanoclusters
1. Introduction
The caseins form the largest protein component in most
milks of industrial significance. A family of phosphoproteins, it
is now generally accepted that their synthesis and assembly
into the casein micelle, the aggregate in which they are found
in milk, occur in the Golgi apparatus of the mammary gland
[1
&
]. The mechanism of that assembly has been the subject of
much speculation and several alternative models have been
proposed. Because several papers [2
&&
,3–6] on one of these
models have appeared in the last couple of years, it seems
appropriate now to critically scrutinize those models and test
them against the restrictions and requirements placed on them
by the known physical and technological behaviour of the
casein micelle system.
2. Casein and casein micelle properties
An excellent summary of this behaviour by Fox [7
&&
]forms
a substantial platform for this discussion. Particular crucial
features to be met by any micelle model are that they ensure
the stability and integrity of the micelle but allow its
destabilization by any of the routes exploited commercially,
and that they take cognizance of the physicochemical
properties of the caseins and employ all of these sensibly in
any proposed mechanism of micellar assembly and formation.
Any model cannot be species specific but should recognize that
casein micelles are found in the milks of all mammals and that
the compositions of these milks can vary widely in the total
protein concentrations and their relative proportions [8]. The
casein proteins are phosphoproteins and divide themselves into
two groups, the calcium-sensitive and the non-calcium-
sensitive, which also in mixtures prevent or inhibit the
precipitation of the calcium-sensitive group by calcium. In
bovine milk, n-casein is calcium-insensitive and a
S1
,a
S2
and h
are the three calcium-sensitive members. Two or more
analogues of the latter group have been found in all milks
studied at this level of detail [9
&
]. Most milks also have a n-
casein type, though it has been suggested that its role may also
be filled by a dephosphorylated h-casein [10
&
]. The calcium-
sensitive caseins are highly phosphorylated and the phospho-
seryl residues tend to be found in clusters of 2, 3 or 4 such
residues. Martin et al. [9
&
]have compared the amino-acid
sequences of the caseins across species. They note that the
phosphoseryl clusters in a
S1
-andh-caseins are highly
conserved and that despite high rates of mutational change
and sequence diversity, many of the mutations also tend to be
conservative with hydrophobic residues replacing hydropho-
bic. The amphipathic nature of the caseins is thus preserved
across species with each of the caseins showing their own
pattern of segregation into hydrophobic and hydrophilic
regions, the latter containing the phosphoseryl clusters.
Because these features come through so strongly, it is plausible
to anticipate for them a role in the assembly and structure of
the casein micelles and, indeed, to varying extents modellers
have taken this on board.
As to the micellar features and arrangements of the caseins
within the micelles which any satisfactory model must
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E-mail address: brendavi@aol.com.
Current Opinion in Colloid & Interface Science 11 (2006) 148 – 153
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reproduce, chief amongst these must be the location of n-
casein. As noted by Fox [7
&&
],n-casein must be located so as to
be able (1) to stabilize the calcium-sensitive caseins, (2) to
allow rapid and specific hydrolysis by chymosin and similar
proteases and (3) to permit complex formation with whey
proteins when heated in normal milk. The arrangement that
would best suit these requirements is a surface layer of n-
casein, an arrangement that also satisfies the observation that n-
casein content is inversely proportional to micelle size across
the micelle size distribution in bovine milk [11,12] and that the
nmr spectra of the micelles reveal only the C-terminal
macropeptide of n-casein to be mobile at 20 -C[13,14].
A consensus of opinion exists that this outer Fhairy layer_of
n-casein ensures the stability of the casein micelle through a
steric stabilization mechanism [15
&
]. Many of the transport and
optical properties of the micelle dispersion (diffusion, viscosity
etc.) can be described as a function of volume fraction (< 45%)
by treating the micelles as colloidal hard spheres [16]. DeKruif
and co-workers [2
&&
,17] have conjectured that renneting, acid
gelation and ethanol flocculation can be described by treating
the hairy layer as a salted polyelectrolyte brush. Each process
induces collapse or removal of the brush and as a result the
casein micelle exhibits behaviour that is apparently well
described using this adhesive sphere model. Tuinier and
DeKruif [18
&
]have taken this approach further and calculated
a pair potential based on additive contributions from brush
repulsion, electrostatic repulsion and van der Waals attraction,
with again surprisingly good agreement with experiment up to
the onset of gelation. This is surprising and puzzling because in
acid gelation and ethanol-induced flocculation there is evidence
of loss of micellar integrity and changes in micelle structure
which should render the simple solid-sphere approach invalid
[19–21]. Moreover, measurements of zeta potential during
renneting have found this to be halved from some 20 mV to
around 10 mV [22,23] indicating significant electrostatic
repulsion between micelles at the plane of shear, whereas
Tuinier and DeKruif [18
&
]find no significant contribution from
this term to their calculated pair-interaction potential. Incon-
sistencies thus become evident in this adhesive hard sphere
approach on closer inspection; the complexities of micellar
interaction behaviour have yet to be fully described.
The dry matter of bovine casein micelles is ¨94% protein
and ¨6% mineral, referred to collectively as colloidal calcium
phosphate (CCP). This CCP is regarded as the cement which
holds the micelle together, since its removal by EDTA
sequestration of calcium [24] or by dialysis against a calcium
phosphate free buffer [25] results in dissolution of the micelles.
However, micellar integrity is largely maintained when the
calcium phosphate is dissolved out by acidification at room
temperature or slightly higher [26], pointing to the involvement
of other interactions between the caseins. Horne [10
&
]grouped
such interactions under the label hydrophobic but this should
be considered a general term encompassing true hydrophobic
attraction as well as hydrogen bonds. That these play a part in
the internal bonding of the micelle is demonstrated by the
observations of McGann and Fox [27
&
]that the micelles can be
extensively dissociated by urea. That these interactions are of
significant strength in their totality is shown by the recent
measurements by Uricanu et al. [28
&&
]of the elastic properties
of individual micelles by atomic force microscopy, showing in
the pH range 5.6 to 5.0, elastic moduli of several hundred
kiloPascals.
3. Micelle models
Various models of casein micelle structure have been
proposed over the last 50 years and progress has been reviewed
regularly, most recently by Fox [7
&&
]. The most enduring of the
early attempts is the submicelle model which, though with
refinement and tinkering, still remains largely as described by
Slattery and Evard [29] and Slattery [30] with chief elaboration
by Schmidt [31].
In this submicelle model, the caseins first aggregate via
hydrophobic interaction into subunits of 15 – 20 molecules
each. The pattern of interaction is such that it brings about a
variation in the n-casein content of these submicelles. Those
rich in n-casein congregate on the micelle surface, those
submicelles poor or totally deficient in n-casein are located in
the interior of the micelle as depicted in Fig. 1. The elaboration
of Schmidt [31] is to link these interior submicelles by colloidal
calcium phosphate. What has never been explained is what
drives the segregation of the n-casein or why n-casein
κ-rich sub-micelle κ-poor
Calcium
phosphate
Fig. 1. The schematic of the submicelle model of the casein micelle.
D.S. Horne / Current Opinion in Colloid & Interface Science 11 (2006) 148 – 153 149

molecules, having preferred to associate with their own kind to
form these segregated patches in the n-rich submicelles, should
then associate with the other caseins to complete the building
of the submicelle? If we are to have two different kinds of
submicelle, why should one of these be mixed from all the
caseins? Another criticism of this model is the late entry of
calcium phosphate into the assembly process, almost as an
afterthought by Slattery and Evard [29], but as the actual
cement holding together the a
S
- and h-casein hydrophilic
surfaces of the submicelles, as proposed by Schmidt [31], after
the formation of the subunits. Separating the caseins from
calcium and phosphate until this point in the assembly process
is not really possible, since both calcium and phosphate are
involved in the phosphorylation of the protein chain which
occurs immediately post-translation [32 – 34
&
]and presumably
before the association of the chains into submicelles.
Though it seemingly refuses to die, the submicelle model
was effectively killed by the careful electron microscopy
studies of McMahon and McManus [35
&&
]. Early em studies
[36,37] gave pictures of casein micelles with a raspberry-like
appearance and lent support to the submicelle model. Such
structures were shown to be artefacts of sample preparation and
treatment [35
&&
]. Stereo images of casein micelles obtained by
cryo-transmission electron microscopy showed an inhomoge-
neous internal structure within the micelle, but no electron
dense particles larger than 8 –10 nm and with most individual
areas only 2 – 3 nm [35
&&
]. The latest high resolution field-
emission scanning electron microscopy study [38
&
]shows no
evidence of spherical subunits but instead suggests an
organization of the caseins into tubular structures protruding
from the surface and originating from within the micelle. The
micelle surface is thus not smooth but contains gaps between
the substructures. Whether these images are artefacts of the
field-emission technique remains to be seen. What is clear is
that any model of casein micelle assembly has to produce a
structure which has the flexibility to respond to the sample
preparation techniques for electron microscopy in such a way
as to end up as the images presented whether corpuscular,
tubular or a structureless cloud. This in itself could prove a
stringent requirement for any plausible model.
The model produced by Holt [34
&
,2
&&
]shows great corre-
spondence with the transmission electron micrographs of
McMahon and McManus [35
&&
]. Whereas the submicelle model
emphasized the role of hydrophobic interactions in giving rise
to submicelles, the Holt model relies solely on the interactions
between the caseins and calcium phosphate to hold the micelle
together. In the later refinements of this model [2
&&
,4], the
calcium phosphate is in the form of nanoclusters and the
interaction sites on the caseins are the phosphoseryl clusters of
the calcium-sensitive caseins (Fig. 2). Because a
S1
- and a
S2
-
caseins have more than two such clusters, arguably in the case
of a
S1
-casein, they are able to cross-link the nanoclusters into
extended 3-dimensional network structures. This approach is
similar to the dual-binding model of Horne [10
&
]and indeed
forms one pathway envisaged in that polymerization model.
Where the dual-binding and Holt models part company is in the
size of the nanocluster and in the number of phosphate clusters
(or casein molecules) that the surface of the nanocluster can
accommodate.
Holt [2
&&
,4] suggests that the micellar calcium phosphate is
identical in all respects to the calcium phosphate nanocluster
formed when solutions of calcium phosphate and h-casein
phosphopeptide 4P (f1–25) are raised slowly in pH to ¨6.7.
These peptide-based nanoclusters are determined by neutron
and X-ray scattering to be of core radius 2.3 nm, surrounded by
a coating of 49 peptides forming a shell 1.6 nm thick [39].In
the casein micelle, Holt [2
&&
,4] suggests that the core of calcium
phosphate stays the same but is now surrounded by 49 casein
molecules or 49 phosphoseryl clusters in casein molecules.
This works out at 1.6 nm
2
of surface for every phosphoseryl
cluster. This may be possible for the short, still highly charged
casein phosphopeptides which will stick out from the surface
like the polyelectrolyte brush of DeKruif and Zhulina [17] and
provide electrosteric stabilization for the nanocluster, but is
arguably overcrowded for entire protein molecules where the
phosphoseryl clusters are more central and the molecule
αS1-casein (8P)
---- - SerP46-Glu-SerP48- ----- - SerP64-Ile-SerP66-SerP67-SerP68- --------- -SerP75- -------
--- SerP115- -------
αS2-casein (11 or 12P)
--- -SerP8-SerP9-SerP10- --- -SerP16- --------- -SerP56-SerP57-SerP58-Glu-Glu-SerP61- -
------------ -SerP129-Thr-SerP131- ----- -SerP143- -----
β-casein (5P)
-------- -SerP15-Leu-SerP17-SerP18-SerP19- ------- -SerP35- ----------------
κ-casein (1P)
------------------ -SerP149- ------------
Fig. 2. Phosphate residue positions in the bovine caseins, indicating the phosphoseryl clusters. Sequences taken from Swaisgood HE: Chemistry of the caseins. In
Advanced Dairy Chemistry. Volume 1 Proteins, 3rd edn. Edited by Fox PF, McSweeney PLH. New York: Kluwer Academic/Plenum Publishers; 2003: 139 – 201.
D.S. Horne / Current Opinion in Colloid & Interface Science 11 (2006) 148 – 153150

extends on either side of them, giving effectively 100 chains
extending from the surface of the nanocluster core.
Moreover, not all groups agree on the molecular weight of
the peptide-stabilized nanocluster. In contrast to the 200 kDa
total mass of those prepared by Holt et al. [39], Ono et al. [40]
estimated a molecular weight of 18 kDa for a phosphopeptide/
calcium phosphate complex prepared by successive digestion
of casein micelles by pepsin, followed by trypsin, allowing
perhaps for only 4–5 phosphopeptides per nanocluster. Holt
himself in an earlier paper [41] suggested a similar value of
around 7 peptides per micellar calcium phosphate nanocluster.
Holt’s suggestion that the micellar calcium phosphate
particle is equal in all respects to their nanocluster is based
on the prediction that 800 such clusters, acting as scattering
points in an average micelle of radius 100 nm, give a value of
18 nm for their mean spacing or correlation length, just as
measured experimentally by neutron or X-ray scattering [42,3].
The network arises because the multi-functional caseins, a
S1
-
and a
S2
-casein, can cross-link the nanoclusters, as in Fig. 3.
However the two putative clusters on a
S1
-casein are only 14
amino acid residues apart (see Fig. 2 for sequences). Allowing
0.3 nm size per residue, fully extended, this would only mean a
separation of just over 4 nm between linked core surfaces, or
approximately 9 nm centre-to-centre. Since a
S1
-casein will
form the majority of such links in this model structure, being in
the major proportion, it is difficult to see how an average
separation of 18 nm is achieved. Indeed in a
S1
-casein, this
second phosphoseryl cluster is possibly more likely to loop
around and close down another facet of the same nanocluster
core, simply because of its proximity.
There is, however, doubt as to whether the two phospho-
seryl residues at positions 46 and 48 in the bovine a
S1
-casein
are sufficient of themselves to function as an inhibiting
phosphoseryl cluster. Aoki et al. [43] concluded that a
minimum of three phosphoserine residues is required. Holt
[4] suggests that the shortfall is made up by including singleton
phosphoserines from remotely on the same molecule or from
different casein molecules, but this raises issues in the
energetics of folding and rearrangement, of excluded volume
and accessibility which render these possibilities less likely.
All of which would leave network growth and extension in
the Holt model as mainly due to a
S2
-casein, where again doubts
could be raised as to whether the phosphoseryls at positions 129
and 131 comprise a full functional grouping. Reducing the
functionality from 3 to 2 does not prevent the formation of a
three-dimensional network, since the molecules link to the
multi-functional core (be it with 4, 7 or 49 sites) of the calcium
phosphate nanocluster (Fig. 3). The monofunctional h-casein
molecules, of course, close off the facet to which they attach and
prevent further growth in that direction, as illustrated in Fig. 3.
n-casein does not feature in this assembly process because it
does not possess a phosphoseryl cluster grouping with which it
could interact with the nanocluster.
So what controls the size of the casein micelle? DeKruif and
Holt [2
&&
]suggest that growth is due to a balance of the cross-
linking action of the multi-functional calcium-sensitive caseins
and loop formation. We envisage this loop formation to be as
illustrated in Fig. 3 where two dangling phosphoseryl
functionalities at the end of extended chains come to reside
on the same nanocluster core, effectively closing the loop and
terminating growth. The balance and therefore micelle size, or
at least network size, should therefore be a function of the
number or proportion of multi-functional casein molecules in
the system. Loop formation is a random event, and therefore
micelle size should also be random and occur in a range of
sizes. However this loop formation may close off growth
before either the calcium-sensitive caseins are fully incorpo-
rated or the calcium phosphate is completely reduced to its
Alpha
Beta
CaP nanocluster
Fig. 3. Illustration of network formation in the Holt model. Alpha-casein (both a
S1
- and a
S2
-caseins) are shown as bi-functional, beta is monofunctional. The calcium
phosphate nanocluster is drawn as having 4 closure sites for ease of illustration. The content of reactive caseins is 50:50::alpha:beta. The alpha’s bind to different
nanoclusters, acting as bridges to allow the chain to grow. Within the circle, the chain has closed at the left. On the upper right further growth is possible through the
branch developing there. On the lower right, is illustrated a closed nanocluster surrounded by monofunctional beta chains. In random pickup of casein molecules, this
is easily possible. Note how the chain of linked nanoclusters is surrounded by the dangling hydrophobic regions (blue) of the attached caseins. (For interpretation of
the references to colour in this figure legend, the reader is referred to the web version of this article.)
D.S. Horne / Current Opinion in Colloid & Interface Science 11 (2006) 148 – 153 151

stable solution level. Availability of both could and should
trigger the formation of further micelles in that Golgi vesicle,
and indeed pictures often show images of secretory Golgi
vesicles with several micelles [1
&
]. On another tack, if we have
a low proportion of multi-functional casein, as would occur if
a
S2
-casein at 10% of bovine casein molecules was the only
propagator and if the nanocluster itself was of low function-
ality, say binding only 4 phosphoseryl clusters instead of the 49
suggested by Holt [4], then many of the individual nanoclusters
would be satiated with monofunctional caseins and no network
or very limited network formation would take place. We do not
see micelles as small as this in bovine milk, so that were the
conditions to be varied from those set by Holt [4] and who can
presently say that they would not in milks of species other than
the bovine, growth to micelle size must follow another route,
perhaps as suggested by the dual-binding model.
Rather than being only due to loop closure, DeKruif and Holt
[2
&&
]also consider that the major limitation to network growth
arises because of the termination of the formation of nanoclus-
ters. But, if formation of these is the spontaneous thermody-
namic interaction with phosphoseryl clusters [3,4], then surely
the number of nanoclusters will be dependent on the number of
phosphoseryl clusters and, as suggested above, the growth of
the network should be dependent on the proportion of
polyfunctional caseins. There is no reported evidence of micelle
size being controlled by a
S1
-ora
S2
-casein content, rather the
reverse that size is independent of the proportion of these
molecules in the mix [12]. Holt [4] has attempted to calculate
the partition of the caseins between soluble and micellar phases
but since his analysis fails to take into consideration the
functionality of the calcium phosphate core, it cannot provide a
route to calculation of micellar size or micellar size distribution.
The major failing though of this Holt model is that it
provides no substantive role for n-casein and therefore can
provide no indication of how this molecule controls micelle
size or achieves a location where it can control micelle stability.
What is produced in this Holt model of micellar assembly is a
network of linked nanoclusters with each and every strand
surrounded by the sticky hydrophobic peptides of their
calcium-sensitive casein coating, the hydrophobic regions of
a
S1
-, a
S2
- and h-casein casein. The well-documented self-
association properties of these caseins, which make them so
difficult to separate as individual proteins [7
&&
]and which
render them excellent food emulsifiers, neither of which
function was of nature’s intention, are due to these hydrophobic
regions, but the possibility that they too will interact in the
assembly of the micelle is ignored in this Holt model. But,
allowing them to interact would render the Holt model
equivalent to the dual-binding model of Horne [10
&
,44
&&
],
which does go on to provide a mechanism for incorporating
n-casein as a size-limiter and in a surface location.
4. Concluding remarks
A working model should be so constructed as to imitate the
behaviour of the structure represented. Both the subunit model
and the Holt model of casein micelle assembly are muddles.
They reach their ends, a picture of a supposed micellar
structure in a series of leaps through the unknown. Makeshift
and haphazard, they couple intellectual bewilderment with
gross omissions and oversights, attaining their end points in
spite of blunder upon blunder. Both make use of a highly
selected range of the properties of the caseins. The subunit
model relies on the known preference of the caseins for self-
association but imposes on this a rigid framework of
segregative assembly, as discussed, which defies rational
explanation. The demonstration [35
&&
]that the raspberry-like
structure observed in early em studies is largely artefactual
removes the necessity for this rigid segregation. Removing this
and allowing the hydrophobic regions to react randomly
produces the second interaction pathway of the dual-binding
model [10
&
,44
&&
]. In the Holt model, interaction of the
phosphoserine clusters of the caseins with mineral calcium
phosphate is the dominant (indeed only specified) path to
micellar assembly. Again there is a rigid adherence to an
unrealistic and restrictive requirement placed this time on the
size of the calcium phosphate nanocluster but more importantly
in this model, the hydrophobic interactions of the caseins are
disregarded as weak, non-specific, and insignificant. Individ-
ually, perhaps they are, but collectively they are nature’s
Velcro. Moreover, nature has not spent aeons preserving the
hydrophobic domains of the caseins to no purpose. Introducing
interactions of the hydrophobic regions into the Holt model
converts it also into the dual-binding model which does
describe the process of micellar assembly in a plausible,
realistic and rational manner. The opportunity now exists to
refine the dual-binding approach, to devise ways of testing the
model and exploiting it.
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layer. J Colloid Interface Sci 1986;114:513 – 24.
[24] Griffin MCA, Lyster RLJ, Price JC. The disaggregation of calcium-
depleted casein micelles. Eur J Biochem 1988;174:339 –43.
[25] Holt C, Davies DT, Law AJR. Effects of colloidal calcium phosphate
content and free calcium ion concentration in milk serum on the
dissociation of bovine casein micelles. J Dairy Res 1986;53:557 – 72.
[26] Dalgleish DG, Law AJR. pH-induced dissociation of bovine casein
micelles: I. Analysis of liberated caseins. J Dairy Res 1988;55:529 – 38.
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reformed from urea-treated milk. J Dairy Res 1974;41:45 – 53.
An early paper which indicated that calcium phosphate was not the only
Fcement_holding the casein micelle together.
[28
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proteins: an elasticity study based on atomic force microscopy. Langmuir
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Whatever holds the micelle together when the calcium phosphate bonds
are disrupted is demonstrated in this paper to be of significant strength.
[29] Slattery CW, Evard R. A model for the formation and structure of casein
micelles from subunits of variable composition. Biochim Biophys Acta
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[30] Slattery CW. Model calculations of casein micelle size distribution.
Biophys Chem 1977;6:59 – 64.
[31] Schmidt DG. Colloidal aspects of the caseins. Neth Milk Dairy J
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[32] West DW. Energy-dependent calcium sequestration activity in a Golgi-
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[33] West DW, Clegg RA. The influence of calmodulin on calcium
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vesicles from lactating rat mammary gland. Biochem Soc Trans
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The introduction of the Holt model, distinguished for its brevity and lack
of detail.
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electron microscopy. J Dairy Sci 1998;81:2985 – 2993.
The definitive work on the electron microscopy of the casein micelle.
[36] Schmidt DG, Buchheim W. Elektronenmikroskopische untersuchung
der feinstruktur von caseinmicellen in kuhmilch. Milchwiss 1970;25:
596 – 600.
[37] Kalab M, Phibbs-Todd BE, Allan-Wojtas P. Milk gel structure: XIII.
Rotary shadowing of casein micelles for electron microscopy. Milchwiss
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micelle based on high-resolution field-emission scanning electron micros-
copy. Int Dairy J 2004;14:1025 – 1031.
The latest of the microscopy techniques to be employed to visualise the
casein micelle but are its pictures artefactual?
[39] Holt C, Timmins PA, Errington N, Leaver J. A core-shell model of
calcium phosphate nanoclusters derived from sedimentation equilibrium
and small angle X-ray and neutron scattering measurements. Eur J
Biochem 1998;252:73 – 8.
[40] Ono T, Tagaki Y, Kunishi I. Casein phosphopeptides from casein micelles
by successive digestion with pepsin and trypsin. Biosci Biotechnol
Biochem 1998;62:16 – 21.
[41] Holt C. The milk salts and their interaction with casein. In: Fox PF, editor.
Advanced dairy chemistry. Lactose, water, salts and vitamins, vol. 3.
London’Chapman and Hall; 1997. p. 233 – 44.
[42] Hansen S, Bauer R, Lomholt SB, Bruun Qvist K, Pedersen JS, Mortensen
K. Structure of casein micelles studied by small-angle neutron scattering.
Eur Biophys J 1996;24:143 – 7.
[43] Aoki T, Umeda T, Kako Y. The least number of phosphate groups for
cross-linking of casein by colloidal calcium phosphate. J Dairy Sci
1992;75:971 – 5.
[44
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] Horne DS. Caseins, micellar structure. In: Roginski R, Fox PF, Fuquay
JW, editors. Encyclopaedia of dairy sciences. New York’Academic Press;
2002. p. 1902 – 1909.
The dual-binding model of the casein micelle, in detail.
D.S. Horne / Current Opinion in Colloid & Interface Science 11 (2006) 148 – 153 153